$ F = \left[\begin{array}{rr}-2 & 4 \\ 2 & -1 \\ -1 & -2\end{array}\right]$ $ A = \left[\begin{array}{rrr}2 & 1 & 0 \\ 4 & 1 & 2 \\ -2 & 0 & 2\end{array}\right]$ Is $ F+ A$ defined?
Answer: In order for addition of two matrices to be defined, the matrices must have the same dimensions. If $ F$ is of dimension $( m \times  n)$ and $ A$ is of dimension $( p \times  q)$ , then for their sum to be defined: 1. $ m$ (number of rows in $ F$ ) must equal $ p$ (number of rows in $ A$ ) and 2. $ n$ (number of columns in $ F$ ) must equal $ q$ (number of columns in $ A$ Do $ F$ and $ A$ have the same number of rows? Yes Yes No Yes Do $ F$ and $ A$ have the same number of columns? No Yes No No Since $ F$ has different dimensions $(3\times2)$ from $ A$ $(3\times3)$, $ F+ A$ is not defined.